Senate Republican leaders scored a significant victory on Tuesday in the fight to repeal and replace Obamacare by getting a majority of senators to agree to debate a mystery bill.

The path forward remains uncertain at best, with party leadership still forced to navigate internal policy disputes and anger over a disjointed legislative process.

Even if the Senate manages to push a bill through the chamber, it may very well be rejected by conservative Republicans in the House. One such lawmaker suggested to The Daily Beast that his colleagues won’t simply accept a "yes or no" vote on anything the Senate sends them.

“I think it is a binary choice—is that what we’ve heard before? Binary choices are really good in Congress. They work for monkeys and computers?” Rep. Raul Labrador (R-ID) told The Daily Beast. “Oh wait, was I being sarcastic?”

He was.

“No,” he added, when asked if the House will simply swallow what the Senate produces. “You’ve got to give freedom to the states at a minimum. In my opinion, we should get rid of the entire bill—the entire Obamacare—but that’s not going to happen... This is our one chance to repeal Obamacare and to give the states flexibility.”

Reflecting the tough path still ahead, GOP leaders spent little time on self-congratulation following Tuesday’s vote. Instead, they began gaming out the next few days of legislative activity, which will involve consideration of a host of amendments, numerous—potentially tricky —votes, and arcane parliamentary procedures. Making the path even trickier is the impossibly small margin for error with which they must now work.

Just 50 of the 52 Republican senators voted in favor of the procedural measure to open debate on a health care bill, with moderate Sens. Lisa Murkowski (R-AK) and Susan Collins (R-ME) and all Democrats voting against it. Vice President Mike Pence had to be brought in to break the tie and that was after Sen. John McCain (R-AZ) was summoned back to Washington to vote on the measure, just one week after he was diagnosed with brain cancer. McCain was given a hero’s welcome and a standing ovation in the legislative body where he’s served for three decades.

But even as he cast the deciding vote to proceed to debate, he made it clear that his support for the end-product shouldn’t be taken for granted.

“We’ve tried to do this by coming up with a proposal behind closed doors, in consultation with the administration—and then springing it on skeptical members, trying to convince them that it’s better than nothing,” McCain said. “Asking us to swallow our doubts and force it past a unified opposition? I don’t think that is going to work in the end. And it probably shouldn’t.”

Neither Democratic nor Republican lawmakers and aides said on Tuesday that they definitively knew whether the chamber would actually pass a final bill. But the expectations for doing so have notably brightened in recent days.

On Tuesday, Senate Majority Leader Mitch McConnell was able to effectively persuade his members that it was vital to move forward with debate even without knowing exactly what health care legislation the body was to consider. He is expected to make the same pitch for the final vote: encouraging Republicans to get some, any, bill into a conference committee with the House so that the process can simply continue.

What lawmakers will ultimately vote on is not entirely clear, though Republican aides previewed to The Daily Beast a final product that would repeal the individual and employer mandates as well as the tax on medical device manufacturers while leaving in place Obamacare’s Medicaid expansion. Known as a “skinny repeal,” the legislation, according to the Congressional Budget Office, would still leave an estimated 15 million people uninsured by 2026. But, according to aides, it represents the best possible vehicle—at least at this juncture—for the Senate to move forward.

And even that might be an impossible task.

Though Sen. Rand Paul (R-KY) has indicated that he would drop his conservative-minded opposition to a “skinny repeal” bill provided he got a vote on full repeal beforehand, other conservatives—in both houses of Congress—may still vote no. (Labrador told The Daily Beast that he would not support a so-called “skinny repeal.”) On Tuesday night, Paul was already teasing the clean repeal bill, adding it will come to a vote on Wednesday.

Both Collins and Murkowski have remained consistent in their opposition to Senate Republicans’ approach to health care reform both on policy and process. Sen. Shelley Moore Capito (R-W.V.), who dropped prior opposition to side with leadership on Tuesday, said just last week that she would “only vote to proceed to repeal legislation if I am confident there is a replacement plan that addresses my concerns.” It’s not clear if a “skinny repeal” would do that.

McCain has called for a return to a legislative process that involves congressional committees and Democrats. Whether that, or his health, precludes him from backing the final bill is anyone’s guess. In his speech on the Senate floor, he said would consult with his home state’s governor, Doug Ducey, before voting.

Ultimately, however, the threat of being blamed for doing nothing may outweigh specific concerns with the final piece of legislation—whether that’s “skinny repeal” or something else. That’s the card that President Trump has played, successfully, in the run-ups to the House and Senate votes.

“Any senator who votes against starting debate is telling America that you are fine with the Obamacare nightmare,” the president said Monday at the White House.

And momentum is now definitively on the Republican party’s side. Leaders are aiming to finish the process by the end of this week and send a bill to the House, which is scheduled to begin its August recess next week. Speaker Paul Ryan (R-WI) has pledged that the House would remain in session if the Senate sends over a bill.

“We’re going to stay and finish health care,” Ryan previously said.